Experimental Characterization of Correlation-Functions of Random Surfaces by Speckle Measurement and Complementary Algorithm

A method for the extracting the correlation functions of random surfaces is proposed by using the image speckle intensity. Theoretically, we analyse the integral expression of average intensity of the image speckles, and compare it with the pair of Fourier-Bessel-transform-and-the-inversion of the exponential function of the height-height correlation function of the random surfaces. Then the algorithm is proposed numerically to complement the lacking Bessel function factor in the expression of the average speckle intensity, which changes the intensity data into the pair of the Fourier-Bessel-transform. Experimentally, we measure the average image speckle intensities versus the radius of the filtering aperture in the 4f system and extract the height-height correlation function by using the proposed algorithm. The results of the practical measurements for three surface samples and the comparison with those by atomic force microscopy validate the feasibility of this method.